We propose the
implementation of digital quantum simulators in superconducting
architectures, by enhancing standard digital quantum simulation
techniques with complex circuitQED quantum gates. We study the
quantum simulation capability of a realistic superconducting setup,
composed of transmon qubits and microwave resonators. We analyze the
simulated dynamics for interacting spin models [1], and quantum Rabi
and Dicke models [2]. By designing novel collective gates for
superconducting qubits [3], we show that the dynamics of highly
entangled fermionic systems can be recovered [4].